What is 4x^2+24x+9y^2+18y+9=0 ?

The solution to 4x^2+24x+9y^2+18y+9=0 is Ellipse with (h,k)=(-3,-1),a=3,b=2

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4x^2+24x+9y^2+18y+9=0

4 x^{2} + 24 x + 9 y^{2} + 18 y + 9 = 0

(h, k) = (- 3, - 1), a = 3, b = 2

Solution steps

4 x^{2} + 24 x + 9 y^{2} + 18 y + 9 = 0

Rewrite

4 x^{2} + 24 x + 9 y^{2} + 18 y + 9 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{3 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 1), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 1), a = 3, b = 2

2 x^{2} + y^{2} - 4 x - 4 = 0

3 = \frac{x ^{2}}{1} + \frac{y ^{2}}{\frac{1}{4}}

x^{2} - 4 x + 4 y^{2} - 16 y - 4 = 0

9 x^{2} + 4 y^{2} + 42 x - 54 y - 49 = 0

2 z^{2} - 2 z + 1 + y^{2} = 1

What is 4x^2+24x+9y^2+18y+9=0 ?
The solution to 4x^2+24x+9y^2+18y+9=0 is Ellipse with (h,k)=(-3,-1),a=3,b=2